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We address the problem of a multi-user relay network, where multiplesingle-antenna node pairs want to exchange information by using a multipleantenna relay node. Due to the half-duplex constraint of the relay, theexchange of information takes place in two steps. In the first step, the nodestransmit their data to the relay, while in the second step, the relay isbroadcasting the data by using linear and non-linear precoding strategies. Wefocus on the second step in this paper. We first consider the problem ofmaximizing the overall rate achievable using linear and dirty-paper typeprecoding strategies at the relay. Then, we consider minimizing the total powerat the relay subject to individual SINR constraints using the same strategiesat the relay. We show that the downlink-uplink duality does not hold for thesetup considered here, which is a somewhat surprising result. We also show thatthe beamforming strategy which is optimal in the single-pair case performs verywell in the multi-pair case for practically relevant SNR. The results areillustrated by numerical simulations.

Bidirectional multi-pair network with a MIMO relay: Beamforming strategies and lack of duality